How many vertical asymptotes can a rational function have?

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helixl3u · Accepted Answer

Suppose             f              (        x        )              =                  p                  (          x          )                            q                  (          x          )                     where       p          (      x      )       and       q          (      x      )       are polynomials.If       q          (              x        1            )        =    0   and       p          (              x        1            )        ≠    0   then             f              (        x        )             will have a vertical asymptote at       x    =          x      1      .If       q          (              x        1            )        =    0   and       p          (              x        1            )        =    0   then             f              (        x        )             will have a vertical asymptote at       x    =          x      1       if and only if the multiplicity of this zero of       q          (      x      )       is greater than the multiplicity of this zero of       p          (      x      )      .Therefore, the number of zeros is the largest number of vertical asymptotes that can exist of       q          (      x      )      , which is at most the degree of       q          (      x      )      .

How many vertical asymptotes can a rational function have?

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